Hemmer and Stell model - Revision history

Nice and Tidy: Better defined r

2008-07-17T13:57:36Z

Better defined r

← Older revision		Revision as of 15:57, 17 July 2008
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	{{Stub-general}}		{{Stub-general}}
	The '''Hemmer and Stell model''' [[intermolecular pair potential]], <math>\~~Phi~~(r)</math>, is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):		The '''Hemmer and Stell model''' [[intermolecular pair potential]], <math>\Phi_{12}(r)</math>, is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):

	:<math>\~~Phi~~(r) = \~~Phi~~(r)_{\mathrm {repulsive}} + \~~Phi~~(r)_{\mathrm{attractive}}</math>		:<math>\Phi_{12}(r) = \Phi_{12}(r)_{\mathrm {repulsive}} + \Phi_{12}(r)_{\mathrm{attractive}}</math>

	where a short range piece-wise potential		where a short range piece-wise potential
	:<math>		:<math>
	\~~Phi~~(r)_{\mathrm {repulsive}} = \left\{		\Phi_{12}(r)_{\mathrm {repulsive}} = \left\{
	\begin{array}{ll}		\begin{array}{ll}
	\infty & {\rm if} \; r < d \\		\infty & {\rm if} \; r < d \\
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	\end{array} \right.		\end{array} \right.
	</math>		</math>
	where <math>d</math> is the hard core radius, along with a long-range attractive potential;		where <math>r := \|\mathbf{r}_1 - \mathbf{r}_2\|</math>, <math>d</math> is the hard core radius, along with a long-range attractive potential;

	:<math>\~~Phi~~(r)_{\mathrm{attractive}} = -a\gamma \exp (-\gamma r)</math>		:<math>\Phi_{12}(r)_{\mathrm{attractive}} = -a\gamma \exp (-\gamma r)</math>

	where <math>a</math> is a positive constant.		where <math>a</math> is a positive constant.

Nice and Tidy at 13:27, 22 February 2008

2008-02-22T13:27:38Z

← Older revision		Revision as of 15:27, 22 February 2008
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	#[http://dx.doi.org/10.1063/1.1677857 G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' '''56''', pp. 4274-4286 (1972)]		#[http://dx.doi.org/10.1063/1.1677857 G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' '''56''', pp. 4274-4286 (1972)]
	[[category: models]]		[[category: models]]
			[[category: Polyamorphic systems]]

Carl McBride: New page: {{Stub-general}} The '''Hemmer and Stell model''' intermolecular pair potential, $\Phi(r)$ , is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3): : $\Phi(r) = \Phi(r)_{\mathrm {...$

2008-02-22T12:50:49Z

New page: {{Stub-general}} The '''Hemmer and Stell model''' intermolecular pair potential, <math>\Phi(r)</math>, is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3): :<math>\Phi(r) = \Phi(r)_{\mathrm {...

New page

{{Stub-general}}
The '''Hemmer and Stell model''' [[intermolecular pair potential]], <math>\Phi(r)</math>, is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):

:<math>\Phi(r) = \Phi(r)_{\mathrm {repulsive}} + \Phi(r)_{\mathrm{attractive}}</math>

where a short range piece-wise potential
:<math>
\Phi(r)_{\mathrm {repulsive}} = \left\{
\begin{array}{ll}
\infty & {\rm if} \; r < d \\
V_0 \left( \frac{1- (r-d)}{\lambda d} \right)& {\rm if} \; d < r < d(1+ \lambda) \\

0 & {\rm if} \; d( 1+ \lambda) < r
\end{array} \right.
</math>
where <math>d</math> is the hard core radius, along with a long-range attractive potential;

:<math>\Phi(r)_{\mathrm{attractive}} = -a\gamma \exp (-\gamma r)</math>

where <math>a</math> is a positive constant.
==References==
#[http://dx.doi.org/10.1103/PhysRevLett.24.1284 P. C. Hemmer and G. Stell "Fluids with Several Phase Transitions", Physical Review Letters '''24''' pp. 1284 - 1287 (1970)]
#[http://dx.doi.org/10.1063/1.1677857 G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' '''56''', pp. 4274-4286 (1972)]
[[category: models]]

Hemmer and Stell model - Revision history

Nice and Tidy: Better defined r

Nice and Tidy at 13:27, 22 February 2008

Carl McBride: New page: {{Stub-general}} The '''Hemmer and Stell model''' intermolecular pair potential, \Phi(r), is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3): :\Phi(r) = \Phi(r)_{\mathrm {...

Carl McBride: New page: {{Stub-general}} The '''Hemmer and Stell model''' intermolecular pair potential, $\Phi(r)$ , is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3): : $\Phi(r) = \Phi(r)_{\mathrm {...$